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3 years ago

using a table of values determine the solution to the equation below to the nearest fourth of a unit.

Mathematics

2 answers:

DedPeter [7]3 years ago

3 0

Answer:

सॉरी भाई जल्द ही देखिये अलविदाIl existe de nombreux exemples de portfolios d’artistes en ligne. Trouvez-en un et partagez un lien vers celui-ci. En vous basant sur le portfolio, écrivez quelques phrases évaluant l'artiste. S'il y a les réponses d'autres élèves sur le forum de discussion, examinez-les et voyez si vous êtes d'accord ou pas d'accord avec leur opinion sur le travail des artistes.

Hatshy [7]3 years ago

3 0

Answer:

x= -1.25

Step-by-step explanation:

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Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.

Shtirlitz [24]

Answer:

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

Step-by-step explanation:

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

$V=\pi r^2h=256$

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

$S=2\pi rh+2\pi r^2$

To solve this, we can express h in function of r:

$V=\pi r^2h=256\\\\h=\frac{256}{\pi r^2}$

And replace it in the surface equation

$S=2\pi rh+2\pi r^2=2\pi r(\frac{256}{\pi r^2})+2\pi r^2=\frac{512}{r} +2\pi r^2$

To optimize the function, we derive and equal to zero

$\frac{dS}{dr}=512*(-1)*r^{-2}+4\pi r=0\\\\\frac{-512}{r^2}+4\pi r=0\\\\r^3=\frac{512}{4\pi} \\\\r=\sqrt[3]{\frac{512}{4\pi} } =\sqrt[3]{40.74 }=3.44$

The radius that minimizes the surface is r=3.44 cm.

The height is then

$h=\frac{256}{\pi r^2}=\frac{256}{\pi (3.44)^2}=6.88$

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

$S=2\pi rh+2*(2\pi r^2)=2\pi rh+4\pi r^2$

We derive and equal to zero

$\frac{dS}{dr}=512*(-1)*r^{-2}+8\pi r=0\\\\\frac{-512}{r^2}+8\pi r=0\\\\r^3=\frac{512}{8\pi} \\\\r=\sqrt[3]{\frac{512}{8\pi}}=\sqrt[3]{20.37}=2.73$

The radius that minimizes the real surface is r=2.73 cm.

The height is then

$h=\frac{256}{\pi r^2}=\frac{256}{\pi (2.73)^2}=10.92$

The height that minimizes the real surface is h=10.92 cm.

7 0

4 years ago

Did I do this question right?

Hunter-Best [27]

Answer:

yup, it is definitly correct

4 0

4 years ago

Read 2 more answers

Which of the following are equivalent to

Vladimir79 [104]

A, c, d, f
hope this helps you :)

4 0

3 years ago

Read 2 more answers

A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine th

Sidana [21]

So if we look at the cross section
and assume that the amount turned up is the same on both sides

so what we can do is make 1 equation and find the max or vertex

if the sides are legnth x and base is y
2x+y=18

and the cross sectional area is xy

2x+y=18
minus 2x both sides
y=18-2x
sub for y

x(18-2x)=areamax
18x-2x^2=areamax
we have a parabola
-2x^2+18x+0=areamax
to find the max y valie or area, we find the y value of the vertex
but the x value of the vertex is what we are looking for to find the value of x to max the area
for
ax^2+bx+c=y
x value of vertex is -b/2a
-18/2(-2)=-18/-4=9/2=4.5
4.5=x value of vertex

aswer is 4.5in

C is answer